A Newtonian Big-Bang Hierarchical Cosmological Model

Hierarchical cosmology deals with models having multiple clustering in the matter distribution of the Universe. A continuous representation of a hierarchical universe is introduced and applied, within the framework of Newtonian cosmology, to a more or less realistic model. In general, the mean mass-density is a function of both position and size of the volume considered, and generally decreases with increasing radius. (Observationally, de Vaucouleurs has determined p 7 in the range 10 <r < 1027 cm.) Similarly, the Hubble parameter depends on the order of the cluster involved and is, therefore, a function of the density. If a common origin of clusters is assumed, the relative expansion of the niverse may be determined directly from the density-radius relation. For realistic models (big-bang hierarchy with p at the present epoch), a Hubble law characteristic of the' hierarchy and, at least in principle, subject to observational verification is obtained. (For a reasonable choice of parameters, the graph is nearly linear but does' not intersect the origin.) The history of such a big-bang hierarchy is briefly discussed.